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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i3.10
pages 257-266

A Coupled Discrete/Continuum Model for Multiscale Diffusion

J. S. Tello
Division of Engineering, Brown University Providence, RI02912
William A. Curtin
Brown University; École Polytechnique Fédérale de Lausanne (EPFL), Mechanical Engineering 1015 Lausanne, Switzerland

ABSTRACT

A method is developed to model continuum (finite element) and discrete [kinetic Monte Carlo (kMC)] diffusion occurring simultaneously in connected regions of space. The two regions are coupled across an interface using an iterative domain-decomposition approach in which time-dependent boundary conditions are applied on the kMC region (concentration) and on the continuum region (flux). Evolving forward in small time increments permits iterations in the kMC region to be performed only in a narrow band near the interface. An on-the-fly convergence criterion based on the inherent fluctuations in the discrete problem is developed. Application to the decay of a Gaussian concentration profile demonstrates the accuracy and efficiency of the method. Generalizations to more complex problems in two and three dimensions, and with spatially varying diffusivity due to interactions or applied stress fields, are straightforward.


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